Quelques propriétés des estimateurs à noyaux gamma pour des échantillons de petites tailles

Cherfaoui, Mouloud; Boualem, Mohamed; Assani, Djamil; Adjabi, Smaïl

doi:10.16929/as/2015.763.68

Cited by 2 publications

(5 citation statements)

References 4 publications

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“…The aim of this part is to carry out a comparison study of the performances of the normalized gamma kernel estimators, proposed in the paper of Cherfaoui et al (2015), with those obtained with other boundary correction approaches. To do this, we consider the same examples, the same approaches and the same steps simulation treated in Zhang (2010), namely:…”

Section: Comparative Study Between the Boundary Correction Methodsmentioning

confidence: 99%

“…For densities not satisfying the shoulder condition, the author has shown that the gamma kernel estimator has a severe boundary problem and its performance is inferior to that of the boundary kernel estimator. Recently, Cherfaoui et al (2015) were interested in the properties of gamma kernel estimators for finite samples. By simulation studies, the authors analyzed some proprieties of the gamma kernel density estimators for the different variants of the gamma kernel.…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, in order to predict the behavior of the two proposed normalization methods, Cherfaoui et al (2015) carried out a comparative study on finite artificial samples having different size and they illustrated the necessity of the normalization through an application example using Markov chains.…”

Section: Introductionmentioning

confidence: 99%

“…In the present work, we propose to study the effect and the performances of the normalization techniques, given in Cherfaoui et al (2015), on the quality of the gamma kernel estimators at the boundary (at the point x = 0), according to the type of the density to estimate (with or without pole), compared to other existing boundary corrected kernel estimators. Indeed, we give, in first time, some local proprieties of the gamma kernel estimators at the point x = 0.…”

Section: Introductionmentioning

confidence: 99%

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Influence of the density pole on the performances of its gamma-kernel estimator

Cherfaoui¹,

Boualem²,

Aı̈ssani³

et al. 2017

AJAS

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Abstract. In this paper, we aim at highlighting the influence of the density pole on the performances of its gamma-kernel estimator. To do this, we performed a comparative study for the performances of the gamma-kernel estimators with those provided by other bias effect correction techniques at the bounds, using the simulation technique. In conclusion, the results obtained confirm those provided in the literature and show that in some cases the normalization of the gamma estimators can considerably improve local and global performances of the gamma-kernel estimators.Résumé. Dans ce papier, afin de mettre enévidence l'influence du pôle d'une densité sur les performances de son estimateurà noyau gamma, nous avons réalisé uneétude comparative des performances des estimateursà noyau gamma avec ceux fournis par d'autres techniques de correction du biais aux bornes, en utilisant la technique de simulation. Les résultats obtenus montrent que, dans certains cas, la normalisation des noyaux gamma peut améliorer considérablement les performances locales et globales des estimateursà noyau gamma.

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Section: Comparative Study Between the Boundary Correction Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Influence of the density pole on the performances of its gamma-kernel estimator

Cherfaoui¹,

Boualem²,

Aı̈ssani³

et al. 2017

AJAS

Self Cite

View full text Add to dashboard Cite

show abstract

“…From this proposition, one can note that for non-classical kernels, the total mass Λ(n, h, K) = Λ n of f n is positive and fails to be equal to 1 in general see, e.g., Cherfaoui et al (2015). Table 5 permit to observe that Λ n ∈ [0.9, 1.1].…”

Section: Propertiesmentioning

confidence: 98%

The mode-dispersion approach for constructing continuous associated kernels

Dolele-Kpok¹,

Kokonendji²

2017

JAS

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Abstract. We introduce the mode-dispersion approach for constructing the (asymmetric) continuous associated kernels from suitable parametric probability density functions (p.d.f.) that we shall call the type of kernel. This leads us to value the choice of the associated kernel, since it takes into account the support of the unknown density f , to be estimated. All associated kernel density estimators must be without edge effect. For illustrating this, we introduce the extended beta kernel, which is a typical model of kernels with bounded supports. However, in the presence of a large bias of the density estimator, we propose a general but light modification in the same type of the first associated kernel; it leads to improve the mean integrated square error of the new estimator. Some properties of two estimators are investigated and compared, in particular pointwise and global (asymptotical) properties. Several forms of types of kernels and their associated kernel estimators are subsequently examined in detail. Simulation studies are made on three lognormal kernel density estimators for pointing out some behaviors at the boundaries. 1418Résumé. Nous introduisons l'approche mode-dispersion pour la construction des noyaux associés continus (asymétrique) à partir des fonctions de densité de probabilités (f.d.p.) paramétrées que nous appelons type de noyau. Ceci nous conduit à valoriser le choix du noyau associé puisque celui-ci tient compte du support de la densité inconnue f , à estimer. Tous les estimateurs à noyaux associés de densité sont sans effet de bord. Pour illustrer ceci, nous introduisons le noyau associé bêta étendu, qui est un modèle type des noyaux à supports bornés. Cependant, en présence d'un grand biais de l'estimateur à noyaux associés de densité, nous proposons une technique de modification générale mais légère dans le même type du premier noyau associé ; Cela conduit à réduire l'erreur quadratique moyenne intégrée du nouvel estimateur. Certaines propriétés de deux estimateurs sont étudiées et comparées, en particulier des propriétés asymptotiques ponctuelles et globales. Plusieurs formes de types de noyaux et leurs estimateurs à noyaux associés sont ensuite examinés en détail. Des études de simulation sont faites sur trois estimateurs de densité à noyau log-normal pour souligner les comportements aux bords.

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Quelques propriétés des estimateurs à noyaux gamma pour des échantillons de petites tailles

Cited by 2 publications

References 4 publications

Influence of the density pole on the performances of its gamma-kernel estimator

Influence of the density pole on the performances of its gamma-kernel estimator

The mode-dispersion approach for constructing continuous associated kernels

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